LIST OF PUBLICATIONS OF MARIO ABUNDO
Journals/Collections
51. M. Abundo: On First-Hitting Time of a Linear Boundary by Perturbed Brownian Motion.
The Open Mathematics Journal, 2014, Vol. 7, pp 6-8; doi:10.2174/1874117701407010006
50. M. Abundo: One-dimensional reflected diffusions with two boundaries and an inverse firsthitting problem. Stochastic Anal. Appl. 32: 975–991, 2014.
DOI 10.1080/07362994.2014.959595
49. M. Abundo: Investigating the Distribution of the First-Crossing Area of a Diffusion Process
with Jumps Over a Threshold. The Open Applied Mathematics Journal, 2013, 7, 18-28.
DOI: 10.2174/1874114201307010018
48. M. Abundo, M. Abundo: Some Remarks on the First-Crossing Area of a Diffusion Process
with Jumps over a Constant Barrier. Lecture Notes in Computer Science, Computer Aided
Systems Theory.EUROCAST 2013, Part I. vol. 8111, pp. 20-27. Springer Berlin/ Heidelberg,
2013. DOI 10.1007/978-3-642-53856-8
47. M. Abundo: On the representation of an integrated Gauss-Markov process.
Scientiae Mathematicae Japonicae Online, e-2013, 719–723
46. M. Abundo: Solving an inverse first-passage-time problem for Wiener process subject to
random jumps from a boundary. Stochastic Anal. Appl. 31: 4, 695-707 (2013).
ISSN 0736-2994 print/1532-9356 online. DOI: 10.1080/07362994.2013.800358
45. M. Abundo: Some randomized first-passage problems for one-dimensional diffusion
processes. Scientiae Mathematicae Japonicae, 76, No. 1 (2013), 33–46 : e-2013, 33–46.
44. M. Abundo: The double-barrier inverse first-passage problem for Wiener process with random
starting point. Statistics and Probability Letters. vol. 83 (2013), 168-176.
doi: 10.1016/j.spl.2012.09.006.
43. M. Abundo, C. Macci, G. Stabile: Asymptotic results for exit probabilities of stochastic
processes governed by an integral type rate function.
Prob. Math. Statis. Vol. 32, (1), (2012), 25-39.
42. M. Abundo: First-passage time of a stochastic integral process trough a linear boundary.
International Journal of Applied Mathematics (IJAM), vol. 25, No 1, (2012), 41-49.
41. M. Abundo: An inverse first-passage problem for one-dimensional diffusions with random
starting point. Statistics and Probability Letters, 82 (1) (2012), 7-14;
doi.org/10.1016/j.spl.2011.09.005
40. M. Abundo: On the first-passage area of a one-dimensional jump-diffusion process.
Methodol Comput Appl Probab (2013) 15:85–103 (Online First, April 2011).
DOI 10.1007/s11009-011-9223-1.
39. M. Abundo and M. Abundo: The first-passage area of an emptying Brownian queue.
International Journal of Applied Mathematics (IJAM), vol. 24, No 2, (2011), 259-266.
38. M. Abundo: First passage problems for one-dimensional diffusions with random jumps from
a boundary. Stochastic Anal. Appl. 29 (1) (2011), 121- 145.
37. M. Abundo: First-Passage Problems for Asymmetric Diffusions and Skew-diffusion
Processes. Open Systems & Information Dynamics Vol. 16, No. 4 (2009), 325-350.
36. M. Abundo: On the Continuous Diffusion Approximation of Some Discrete Markov Chains.
The Open Applied Mathematics Journal, 2009, 3, 7-13.
35. M. Abundo: On the First Hitting Time of a One-dimensional Diffusion and a Compound
Poisson Process. Methodol. Comput. Appl. Probab. (2010) 12:473–490 (Online First, 2008:
1
DOI10.1007/s11009-008-9115-1).
34. M. Abundo: On the distribution of the time average of a jump-diffusion process
International Journal of Applied Mathematics (IJAM), vol. 21, No. 3 (2008), 447-454.
33. M. Abundo: Some Remarks on the maximum of a one-dimensional diffusion process.
Prob. Math. Statis. Vol. 28 (1) (2008), 107-120.
32. M. Abundo: On first-passage problems for asymmetric one-dimensional diffusions
Lecture Notes in Computer Science, Computer Aided Systems Theory – EUROCAST 2007,
vol. 4739, pp. 179-186, Springer Berlin/ Heidelberg, 2007.
31. M. Abundo: Limit at zero of the first-passage time density and the inverse problem for onedimensional diffusions Stochastic Anal. Appl., 24 (2006), 1119-1145.
30. M. Abundo: The arc-sine law for the first instant at which a diffusion process equals the
ultimate value of a functional Int. J. Pure Appl. Math., 30 (1), 13-22 (2006).
29. M. Abundo: Qualitative behaviour of the first-passage-time density of a one-dimensional
diffusion over a moving boundary Scientiae Mathematicae Japonicae, 64, No. 2 (2006), 199216, : e-2006, 641-658.
28. M. Abundo: Stopping a stochastic integral process as close as possible to the ultimate value of
a functional Scientiae Mathematicae Japonicae , 60 No. 3 (2004), 475-479,
: e-2004, (10) 417- 421.
27. M. Abundo: On the risk of extinction for a population subject to a random markov evolution
with jumps Open Sys. & Information Dyn. 11, 105-121 (2004).
26. M. Abundo: On the first-passage time of diffusion processes over a one-sided stochastic
boundary Stochastic Analysis and Applications vol. 21, No. 1, 1-23 (2003).
25. M. Abundo: Some comparison results of solutions of diffusion and jump-diffusion equations.
Advances and Applications in Statistics vol. 2 (1), 51-78 (2002).
24. M. Abundo: Some conditional crossing results of Brownian motion over a piecewise-linear
boundary Statistics and Probability Letters, vol. 58 (2), 131-145 (2002).
23. M. Abundo, L. Accardi, N. Rosato, L. Stella: Analysing protein energy data by a stochastic
model for cooperative interactions: comparison and characterization of cooperativity
J. Math. Biol. 44, 341-359 (2002).
22. M. Abundo: On first-passage-times for one-dimensional jump-diffusion processes.
Prob. Math. Statis., vol 20, Fasc. 2, 399-423 (2000).
21. M. Abundo: Some results about boundary crossing for Brownian motion. Ricerche di
Matematica vol. L, (2), 283-301 (2001).
20. M. Abundo: On first-crossing times of one-dimensional diffusions over two time-dependent
boundaries. Stochastic Analysis and Applications. , 18 (2), 179-200 (2000).
19. M. Abundo: On some properties of one-dimensional diffusion processes
on an interval Prob. Math. Statis., vol 17, Fasc. 2 (1997), pp. 235-268.
18. M. Abundo, P. Baldi, L. Caramellino : A diffusion approximation which models
hierarchic interactions in cooperative biological systems Open Systems & Information
Dynamics 5: 1-23, (1998).
17. M. Abundo, L. Accardi, N. Rosato, L. Stella: A stochastic model for the
cooperative relaxation of proteins, based on a hierarchy of bonds between aminoacidic
residues Math. Models and Meth. in Appl. Sci., vol. 8, No. 2 (1998) 327-358.
16. M. Abundo, L. Accardi, N. Rosato, G. Mei, A. Finazzi Agrò :
A stochastic model for the sigmoidal behaviour of cooperative biological systems
Biophysical Chemistry 58 (1996) 313-323.
15. M. Abundo, L. Caramellino : Some remarks about a Markov chain which models
cooperative biological systems Open Systems & Information Dynamics
Vol. 3 No 3 (1995) 325-343.
14. M. Abundo, L. Accardi, N. Rosato : A Markovian model for cooperative interactions
2
in proteins Math. Models and Meth. in Appl. Sci. Vol. 5, No. 6 (1995) 835-863.
13. M. Abundo, C. Rossi : Some scenario Analyses for HIV epidemic
Statistica Applicata, vol. 6, n. 2, 121-136 (1994).
12. M. Abundo, C. Rossi: A stochastic model of the impact of genetic variability of HIV on
the immune system in infected patients In Modeling the AIDS Epidemic
E. H. Kaplan and M.L. Brandeau (Editors), 481-498, Raven Press, New York, 1994.
11. M. Abundo, L. Accardi, A. Auricchio : Hyperbolic automorphisms of Tori and
pseudo-random sequences Calcolo vol. 29, 213-240 (1992).
10. M. Abundo, C. Rossi, O. Rubiu : Estimation of parameters for a stochastic model of
tumoral cells treated with anticancer agents J. Exp. Clin. Cancer Res., 12, 2, 81-90 (1993).
9. M. Abundo : A stochastic model for predator-prey systems: basic properties,stability
and computer simulation J. Math. Biol. 29: 495-511 (1991).
8. M. Abundo, L. Accardi : Squeezing corrections to the Bloch equations
Il Nuovo Cimento vol. 106 B, n. 2, 187-194 (1991).
7. M. Abundo, G. Mele : Absolutely continuous invariant measures for expanding maps of a
d-dimensional unit cube in Rd and their entropy Note di Matematica vol X, n.2. 217-233
(1990). Note di Matematica vol X, n.2. 217-233 (1990).
6. M. Abundo, C. Rossi : Numerical Simulations of a stochastic model for cancerous cells
submitted to chemoterapy J. Math. Biol. (1989) 27: 81,90.
5. M. Abundo : An almost sure invariance principle for the maps Sa(x)=ax(1-x) in the interval
[0,1] Le Matematiche, Vol. XLII (1987)- Fasc. I-II, 11-18 .
4. M. Abundo : Entropy and characteristic exponents for the quadratic map on the unit interval
Note di Matematica vol. VII (1987), 47-54.
3. M. Abundo : A remark about topological and measure entropy for a class of maps of the
interval [0,1] Rendiconti del Circolo Matematico di Palermo Serie II, Tomo XXXV (1986),
456-465.
2. M. Abundo, B. Tirozzi : A central limit theorem for expanding maps of the interval [0,1]
Boll. Un. Mat. Ital. (6) 4-A (1985), 237-244.
1. M. Abundo, B. Tirozzi : The central limit theorem for a class of maps of the interval [0,1]
Boll. Un. Mat. Ital. (6) 3-B (1984), 25-37.
Proceedings of conferences with referee
17. M. Abundo, M. Abundo: Some Remarks on First-passage Times for Integrated Gauss-Markov
Processes. In: Computer Aided System Theory (Quesada-Arenciba, Rodrigues, Moreno-Diaz
R. jr., Moreno-Diaz R. eds.) Extended Abstracts of the 15th International Conference on
Computer Aided System Theory, EUROCAST 2015, IUCTC.
Universidad de Las Palmas de Gran Canaria, pp. 45-46.
16. M. Abundo: An inverse first-passage problem for one-dimensional diffusions reflected
between two boundaries. In: SMTDA 2014 (Christos H. Skiadas ed.) Book of Abstracts of
the 3rd Stochastic Modeling Techniques and Data Analysis International Conference.
Lisbona, Portugal, June 11-14, 2014. Published by: ISAST: Intern. Soc. for Advanc. of Science
and Technology. Book ISBN: 978-618-81257-5-9; e-Book ISBN: 978-618-81257-6-6, pp. 6-7.
Conference Proceedings: pp. 1-12.
15. M. Abundo, M. Abundo: Some remarks on the first-crossing area of a diffusion process with
jumps over a constant boundary. In: Computer Aided System Theory (Quesada-Arenciba,
Rodrigues, Moreno-Diaz R. jr., Moreno-Diaz R. eds.) Extended Abstracts of the 14th
International Conference on Computer Aided System Theory, EUROCAST 2013, IUCTC
Universidad de Las Palmas de Gran Canaria, ISBN-13: 978-84-695-6971-9, pp. 5-6.
3
14. M. Abundo, M. Abundo: On the first-passage area of an emptying Brownian queue.
in: Computer Aided System Theory (Quesada-Arenciba, Rodrigues, Moreno-Diaz R. jr.,
Moreno-Diaz R. eds.) Extended Abstracts of the 13th International Conference on Computer
Aided System Theory, EUROCAST 2011, IUCTC Universidad de Las Palmas de Gran Canaria,
ISBN: 978-84-693-9560-8, pp. 70-71
13. M. Abundo: On First-passage Problems for one-dimensional diffusions with random jump
reflection at a boundary. In: R. Trappl (Ed.) Cybernetics and Systems 2010, pp 163168, Austrian Society for Cybernetics Studies,Vienna, 2010.
12. P. Abundo, N. Rosato and M. Abundo A Stochastic Model for Infective Events in Operating
Room Caused by Air Contamination.In: Proceedings of BIOCOMP 2007, CP1028, Collective
Dynamics: Topics on Competition and Cooperation in the Biosciences (L.M. Ricciardi, A.
Buonocore, and E. Pirozzi eds.), American Insitute of Physics, 2008, pp. 198-209.
11. M. Abundo: On First-passage Problems for Asymmetric Diffusions.
In: R. Trappl (Ed.) Cybernetics and Systems 2008 , pp 238-243, Austrian Society for
Cybernetics Studies,Vienna, 2008.
10. M. Abundo: On first-passage problems for asymmetric one-dimensional diffusions
in: Computer Aided System Theory (Quesada-Arenciba, Rodrigues, Moreno-Diaz R. jr.,
Moreno-Diaz R. eds.) Extended Abstracts of the 11th International Conference on Computer
Aided System Theory, EUROCAST 2007, IUCTC Universidad de Las Palmas de Gran Canaria,
ISBN: 978-84-690-3603-7, 66-67
9. M. Abundo: The inverse first-passage time problem for one-dimensional diffusions
In: R. Trappl (Ed.) Cybernetics and Systems 2006 , pp 226-231, World Scientific, 2006.
8. M. Abundo: Extinction risk for a population driven by a jump-diffusion equation
In: R. Trappl (Ed.) Cybernetics and Systems 2004 , pp 169-175, World Scientific, 2004.
7. M. Abundo: On comparison of solutions of diffusion and jump-diffusion equations
In: R. Trappl (Ed.) Cybernetics and Systems 2002 , pp 307-312, Austrian Society for
Cybernetics Studies, Vienna, 2002.
6. M. Abundo: On boundary up-crossing for Brownian motion. In: R. Trappl (Ed.) Cybernetics
and Systems 2000 , pp 295-300, Austrian Society for Cybernetics Studies, Vienna, 2000.
5. M. Abundo: Some remarks on first-crossing-time problem for one-dimensional diffusion
processes. In: R. Trappl (Ed.) Cybernetics and Systems '98 , pp 384-389, Austrian Society
for Cybernetics Studies, Vienna, 1998.
4. M. Abundo: Diffusion approximation of discrete Markov chains with Binomial-like
transition probabilities In: R. Trappl (Ed.) Cybernetics and Systems '96 ,
pp 508-513, Austrian Society for Cybernetics Studies, Vienna, 1996.
3. M. Abundo: Analysis of noise in cooperative systems in Biology
In: R. Trappl (Ed.) Cybernetics and Systems '94, pp 823-830, World Scientific, 1994.
2. M. Abundo: A stochastic model for protein aggregation
In: Topics on Biomathematics, I. Barbieri et Al. (Editors), 113-118, World Scientific, 1993.
1. M. Abundo: On the non-exit problem for some stochastic dynamical systems
In: R. Trappl (Ed.) Cybernetics and Systems Research '92 , 837-844, World Scientific, 1992.
Technical reports
5. M. Abundo: Sequencing DNA fragments by using a simulated annealing algorithm
Technical Report Centro Matematico V. Volterra N.46, July 90.
4. M. Abundo: The simulated annealing algorithm viewed as an iterated function system
Technical Report Centro Matematico V. Volterra N.45, July 90.
3. M. Abundo: Proprietà di trasformazioni sull' intervallo [0,1]
4
Technical Report Dipartimento di Matematica II Università di Roma (1986) .
2. M. Abundo, S. Ghinami, B. Tirozzi: 1/f noise for a stochastic dynamic of a one dimensional
lattice spin system Technical Report Dipartimento di Matematica II Università di Roma,1985.
1. M. Abundo: Equivalenza tra l'ensemble canonico e l'ensemble di Gibbs per opportuni
campi di Gibbs Estratto della Tesi di Laurea, 1979.
Preprints
1. M. Abundo: On the first-passage time of an integrated Gauss-Markov process. Preprint 2015.
arXiv:1506.01155
2. M. Abundo: A randomized first-passage problem for drifted Brownian motion subject to hold
and jump from a boundary. Preprint 2015 arXiv:1509.03448
Books
1. M. Abundo: Esercizi e temi d’esame di Calcolo delle Probabilità e Statistica.
Aracne Editrice, Roma, II edizione, 2006 (ISBN 88-548-0493-2).
2. M. Abundo: Esercizi e problemi di Analisi Matematica 1. Con brevi richiami di teoria.
Aracne Editrice, Roma, 2007 (ISBN 978-88-548-1300-7)
5